LEC12 Discrete Dist Wrap-up

LEC12 Discrete Dist Wrap-up - Three Commonly Used...

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Three Commonly Used Probability Distributions for Discrete Random Variables Dist Random Var. Possible Values Probability Distribution Para- meters Mean Var Binomial r.v. X = number of successes in n independent trials X= 0,. ..,n N x p p x N x - - ( ) 1 n= #trials p= P(succ ess) np np(1-p) Geomet- ric r.v. X = number of failures until first success X = 1,2,. . ( 29 1 1 - - p p x p= P(succ ess) 1 p ( 29 1 2 - p p Poisson r.v. X = number of events in the interval X = 0, 1, . .. f x e x x ( ) ! = - λ λ =E(X) λ λ
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10% of fires calls are false alarms. Find the probability that, out of 5 calls, there are 5 real fires. 10% of fires calls are false alarms. Find the probability of exactly 6 calls to the first false alarm. On average 3.2 fire calls are received per hour. Find the probability that at least one call is received in an hour. 1% of components are defective. I sample 5. Find the probability of at least one defective in the sample. 2
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LEC12 Discrete Dist Wrap-up - Three Commonly Used...

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